NUMERICAL ASPECTS OF MULTIVARIATE NORMAL PROBABILITIES IN ECONOMETRIC MODELS*

The role of Multivariate Normal Probabilities in Econometric Models has in the past been somewhat restrictive because of the unavailability of useful computational formulas. Using the author's recent integral representations for the Multivariate Normal Probability Integral, ThaI (1973) and (1975), highly accurate and efficient computational formulas are now available for computing normal probabilities of dimension up to 6. These formulas have direct application to the Maximum Likelihood procedures which are of interest in econometric modelling. 1. INTRODUCTORY SUMMARY Prior to 1972 and after years of considerable effort, the only known general representation for multivariate normal upper and lower probabilities consisted of Pearson's tetrachoric series (Kendall, 1941) which is well-known to be computa-tionally unattractive for dimension K>2. A reasonably complete bibliography relating to rnultivariate normal probabilities up to 1972 can be found in Johnson and Kotz (1972). Milton (1972) applied a method based on a multidimensional iterated Simpson's quadrature to the customary iterated form for either an upper or lower probability integral. Milton's computerized procedure, however, appeai